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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium

## Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibriumAdd to your list(s) Download to your calendar using vCal - Anton Arnold (Technische Universität Wien)
- Monday 10 January 2022, 13:30-14:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact nobody. FKTW02 - Frontiers in analysis of kinetic equations We are concerned with finding Fokker-Planck equations in whole space with the fastest exponential decay towards a given equilibrium. For a prescribed, anisotropic Gaussian we determine a non-symmetric Fokker-Planck equation with linear drift that shows the highest exponential decay rate for the convergence of its solutions towards equilibrium. At the same time it has to allow for a decay estimate with a multiplicative constant arbitrarily close to its infimum. This infimum is 1, corresponding to the high-rotational limit in the Fokker-Planck drift. Such an “optimal” Fokker-Planck equation is constructed explicitly with a diffusion matrix of rank one, hence being hypocoercive. The proof is based on the recent result that the $L^{2$-propagator norms of the Fokker-Planck equation and of its drift-ODE coincide.
Finally we give an outlook onto using Fokker-Planck equations with t-dependent coefficients.
References:
A. Arnold, B. Signorello: Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium, preprint 2021.
A. Arnold, C. Schmeiser, B. Signorello. Sharp decay estimates and $L2$-propagator norm for Fokker-Planck equations with linear drift, preprint 2020.
This talk is part of the Isaac Newton Institute Seminar Series series.
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